Singapore Math in the Netherlands Day 3

Singapore Math in Rotterdam 3Opleiding Singapore rekenspecialist

This set of slides cover two presentations made on the final day:

• The Spiral Curriculum

• Enrichment Lessons

De structuur van het curriculum onderzoeken en begrijpen hoe de rekenconcepten zorgvuldig op elkaar aansluiten.

Weten hoe verrijking is onderbracht in het programma en hoe betrokkenheid van leerlingen wordt vergroot door gebruik te maken van activiteiten gericht op exploratie, onderzoek, leren door te doen, interactie, reflectie en meer.

Singapore Math in Rotterdam 3Opleiding Singapore rekenspecialist

Review of Day 2 and Going AheadLet’s solve another problem using the model method. Today our focus is on fractions and area and use these to study the idea of the spiral curriculum. We will also look at some enrichment lessons.

Materials developed by Poon Yain Ping

210

5

1

8

3

Mrs Hoon made some cookies to sell. of them were chocolate cookies and the rest

were almond cookies. After selling 210 almond cookies and of the chocolate

cookies, she has of the cookies left.

How many cookies did Mrs Hoon sell?

4

3

6

5

5

1

210

5

1

8

3210

40

7

5

1

8

3

3040

1

96040

32

5

4

Mrs Hoon sold 960 cookies.

Mrs Hoon made some cookies to sell. of them were chocolate cookies and the rest

were almond cookies. After selling 210 almond cookies and of the chocolate

cookies, she has of the cookies left.

How many cookies did Mrs Hoon sell?

4

3

6

5

5

1

The Spiral Approach

Yeap Ban Har, Ph.D.

Marshall Cavendish InstituteSingapore

[email protected]

The Process of Education“A curriculum as it develops should revisit this basic

ideas repeatedly, building upon them until the student had grasped the full formal apparatus that

goes with them.”Bruner 1960

Adding & Subtracting FractionsThis is learned over a period of four years – from grade two to grade five. This is an example of the

spiral approach adopted in the Singapore curriculum. It is not up to textbook authors. It is

based on the national curriculum.

Key Ideas in Fractions

How are these taught? Let’s take a look.

Fraction is introduced in Grade 2.Why are the terms numerator and denominator introduced only in Grade 3?Can you explain this using one of the theoretical underpinnings of Singapore Math?

Please prepare a set of digits 0 to 9 for the activities.

Scarsdale Middle School New York

The Anchor Problem – to make a correct division sentence using one set of digit tiles 0 to 9. Why do you think the teacher provided the restriction of not repeating any of the digits?

Students were given time to make some sentences on their own. It was evident that the students were already familiar with the algorithm. The purpose of this lesson was for students to make sense of the algorithm. Three approaches were used by the students.

First, the teacher wanted to discuss an incorrect use of notation. One pair has thought that 2/0 = 2 and made the sentence

8/4 ÷ 1 = 2/0This example is interesting because it involves the idea of division by 1 which results in the two fractions being equal.

It was agreed that 8/4 = 2 and that the right-hand side is equal to 2.

Other students offered that 2 can also be written as 2/1 and, incorrectly 2 (2/0). The teacher explained that 2/0 is not 1. 2/1 is. And that division by zero is not defined.

Subsequently, students offered the right-hand side can be 4/2 and 6/3. 4/2 was rejected because they realized the condition of the problem – no repetition of digits.

The first explanation a student gave for the algorithm is the fact that 2 fourths shared equally by 3 is equal to each getting 1/3 of 2 fourths.

The second explanation was based on the idea of division of whole numbers. If 2 divided by 2 is 1 then 2 fourths divided by 2 is 1 fourth. If 4 divided by 2 is 2 then 4 fourths divided by 2 is 2 fourths. The rest of the lesson was focused on the whole class grasping these two ideas.

In discussing the other responses forwarded by the students, the teacher challenged the students to use the second method to explained cases such as 8 fourths divided by 6 where 8 is not divisible by 6.

In the case of ¾ divided by 8, students were able to suggest changing the numerator to 24, writing ¾ as 24/32 before dividing by 8 since 24 is divisible by 8.

The third approach used was the bar model that the students have become familiar with. The teacher was pleased that a student who seemed unsure of himself found his voice to explain to the class why 1/5 ÷ 4 = 1/20. The lesson ended with students reflecting on the methods used to explain division of a fraction by a whole number.

Think of two digits. Use the digits to make two numbers. First, the first digit be the tens and second digit be the ones. So if you think of 4 and 5, the number is 45 (not 54). Then, add the digits to make a second number. So 4 and 5 make 9. Finally find the difference between the two numbers (45 and 9).

Reference

www.banhar.blogspot.com

TIMSS 2007 Europe

Advanced

Intermediate

Low

High

Latv

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Eng

land

Russ

ia

111616

444848

818179

979594

Grade 4

TIMSS 2007 EuropeTrends in International Mathematics and Science Studies

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10

42

77

94

Hu

ngary

9

35

67

88

Arm

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8

28

60

84

Denm

ark

7

36

76

95

Neth

erl

and

s

7

42

84

98

Germ

any

6

37

78

96

Italy

6

29

67

91

Advanced

Intermediate

Low

High

Slo

venia

Slo

vak

Rep

Sco

tland

345

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676263

928888

Grade 4


Inte

rnati

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5

26

67

90A

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3

26

69

93

Sw

ed

en

3

24

68

93

Ukr

ain

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2

17

50

79

Cze

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2

19

59

88

Norw

ay

2

15

52

83

Georg

ia

1

10

35

67

Sin

gapore

41

74

92

98

Advanced

Intermediate

Low

High

Latv

ia

Eng

land

Russ

ia

111616

444848

818179

979594

Grade 4


Kaza

khst

an

19

52

81

95Li

thu

ania

10

42

77

94

Hu

ngary

9

35

67

88

Arm

en

ia

8

28

60

84

Denm

ark

7

36

76

95

Neth

erl

and

s

7

42

84

98

Germ

any

6

37

78

96

Italy

6

29

67

91

Singapore Math in the Netherlands Day 3

Education

Transcript of Singapore Math in the Netherlands Day 3